IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v49y2020i3d10.1007_s00182-020-00706-4.html
   My bibliography  Save this article

Cyclic dominance in a two-person rock–scissors–paper game

Author

Listed:
  • Liliana Garrido-da-Silva

    (Centro de Matemática da Universidade do Porto (CMUP))

  • Sofia B. S. D. Castro

    (Centro de Matemática da Universidade do Porto (CMUP)
    Centro de Economia e Finanças (Cef.UP))

Abstract

The Rock–scissors–paper game has been studied to account for cyclic behaviour under various game dynamics. We use a two-person parametrised version of this game. The cyclic behaviour is observed near a heteroclinic cycle, in a heteroclinic network, with two nodes such that, at each node, players alternate in winning and losing. This cycle is shown to be as stable as possible for a wide range of parameter values. The parameters are related to the players’ payoff when a tie occurs.

Suggested Citation

  • Liliana Garrido-da-Silva & Sofia B. S. D. Castro, 2020. "Cyclic dominance in a two-person rock–scissors–paper game," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 885-912, September.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00706-4
    DOI: 10.1007/s00182-020-00706-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-020-00706-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-020-00706-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-659, September.
    2. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    3. Michael D. Noel, 2007. "Edgeworth Price Cycles: Evidence From The Toronto Retail Gasoline Market," Journal of Industrial Economics, Wiley Blackwell, vol. 55(1), pages 69-92, March.
    4. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
    5. Josef Hofbauer & Sylvain Sorin & Yannick Viossat, 2009. "Time Average Replicator and Best-Reply Dynamics," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 263-269, May.
    6. repec:dau:papers:123456789/1014 is not listed on IDEAS
    7. Arnold, Lutz G., 2000. "Stability of the Market Equilibrium in Romer's Model of Endogenous Technological Change: A Complete Characterization," Journal of Macroeconomics, Elsevier, vol. 22(1), pages 69-84, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
    3. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    4. José Pedro Gaivão & Telmo Peixe, 2019. "Periodic attractor in the discrete time best-response dynamics of the rock-paper-scissors game," Working Papers REM 2019/0108, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    5. Jos'e Pedro Gaiv~ao & Telmo Peixe, 2019. "Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game," Papers 1912.06831, arXiv.org.
    6. José Pedro Gaivão & Telmo Peixe, 2021. "Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game," Dynamic Games and Applications, Springer, vol. 11(3), pages 491-511, September.
    7. Kováč, Eugen & Schmidt, Robert C., 2014. "Market share dynamics in a duopoly model with word-of-mouth communication," Games and Economic Behavior, Elsevier, vol. 83(C), pages 178-206.
    8. Mariano Tappata, 2009. "Rockets and feathers: Understanding asymmetric pricing," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 673-687, December.
    9. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    10. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2021. "An Experimental Investigation of Price Dispersion and Cycles," Journal of Political Economy, University of Chicago Press, vol. 129(3), pages 789-841.
    11. Rauh, Michael T., 2009. "Strategic complementarities and search market equilibrium," Games and Economic Behavior, Elsevier, vol. 66(2), pages 959-978, July.
    12. Chakrabarti, Anindya S. & Lahkar, Ratul, 2017. "Productivity dispersion and output fluctuations: An evolutionary model," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 339-360.
    13. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, vol. 112(2), pages 232-260, October.
    14. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    15. Firgo, Matthias & Pennerstorfer, Dieter & Weiss, Christoph R., 2015. "Centrality and pricing in spatially differentiated markets: The case of gasoline," International Journal of Industrial Organization, Elsevier, vol. 40(C), pages 81-90.
    16. Anderson, Edward & Holmberg, Pär, 2018. "Price instability in multi-unit auctions," Journal of Economic Theory, Elsevier, vol. 175(C), pages 318-341.
    17. Samuel de Haas, 2019. "Do pump prices really follow Edgeworth cycles? Evidence from the German retail fuel market," MAGKS Papers on Economics 201913, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    18. Erik Brockbank & Edward Vul, 2021. "Formalizing Opponent Modeling with the Rock, Paper, Scissors Game," Games, MDPI, vol. 12(3), pages 1-20, September.
    19. Timothy N. Cason & Shakun D. Mago, 2010. "Costly Buyer Search In Laboratory Markets With Seller Advertising," Journal of Industrial Economics, Wiley Blackwell, vol. 58(2), pages 424-449, June.
    20. Roger Waldeck & Eric Darmon, 2006. "Can boundedly rational sellers learn to play Nash?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(2), pages 147-169, November.

    More about this item

    Keywords

    Price setting; Rock–scissors–paper game; Cyclic dynamics; Stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00706-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.